Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 444, 688, 454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 444, 688, 454 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 444, 688, 454 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 444, 688, 454 is 2.
HCF(444, 688, 454) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 444, 688, 454 is 2.
Step 1: Since 688 > 444, we apply the division lemma to 688 and 444, to get
688 = 444 x 1 + 244
Step 2: Since the reminder 444 ≠ 0, we apply division lemma to 244 and 444, to get
444 = 244 x 1 + 200
Step 3: We consider the new divisor 244 and the new remainder 200, and apply the division lemma to get
244 = 200 x 1 + 44
We consider the new divisor 200 and the new remainder 44,and apply the division lemma to get
200 = 44 x 4 + 24
We consider the new divisor 44 and the new remainder 24,and apply the division lemma to get
44 = 24 x 1 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 444 and 688 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(44,24) = HCF(200,44) = HCF(244,200) = HCF(444,244) = HCF(688,444) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 454 > 4, we apply the division lemma to 454 and 4, to get
454 = 4 x 113 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 454 is 2
Notice that 2 = HCF(4,2) = HCF(454,4) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 444, 688, 454?
Answer: HCF of 444, 688, 454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 444, 688, 454 using Euclid's Algorithm?
Answer: For arbitrary numbers 444, 688, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.